Hi, theres a lot of nice looking demonstrations of 4D projection showing tesseracts and other wonderful shapes. I'm trying to make a visualisation of a tesseract and I couldn't find anything explicitly describing the maths involved on google...
How (preferably in pseudo code) does one project a point in 4D space into 3D space?
thanks in advance!
The straight ahead answer is: define a 3D rectangular segment in your N space to be the view-port and focus and then for points of interest shoot rays toward the focus, their intersection with the view-port (if any) is the projected location...
However for the purposes of a visualization this may not be the easiest or best thing to do. You have the freedom to choose an arbitrary mapping, and you may want to impose some kind of symmetry on the high dimensional object and take advantage of that somehow (say the CM of the object must be located at the origin, and you will map the first three dimensions directly into 3-space and then scale the resulting vector by the fourth dimension (no idea if this will look good, BTW, but I think that is would result in the usual toothpick-cube-in-a-cube modeling of a tesseract)).